Relevant bibliographies by topics / Symplectic and Poisson geometry / Dissertations / Theses
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Dissertations / Theses on the topic 'Symplectic and Poisson geometry'

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Published: 11 March 2023

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1

Martino, Maurizio. "Symplectic reflection algebras and Poisson geometry." Thesis, University of Glasgow, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426614.

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2

Remsing, Claidiu Cristian. "Tangentially symplectic foliations." Thesis, Rhodes University, 1994. http://hdl.handle.net/10962/d1005233.

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This thesis is concerned principally with tangential geometry and the applications of these concepts to tangentially symplectic foliations. The subject of tangential geometry is still at an elementary stage. The author here systematises current concepts and results and extends them, leading to the definition of vertical connections and vertical G-structures. Tangentially symplectic foliations are then characterised in terms of vertical symplectic forms. Some significant particular cases are discussed.
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3

Kirchhoff-Lukat, Charlotte Sophie. "Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283007.

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This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that L
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4

Costa, Paulo Henrique Pereira da 1983. "Difusões em variedades de poisson." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306283.

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Orientador: Paulo Regis Caron Ruffino<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-13T23:01:19Z (GMT). No. of bitstreams: 1 Costa_PauloHenriquePereirada_M.pdf: 875708 bytes, checksum: 8862a1813f1bb85b5d0269462a80501e (MD5) Previous issue date: 2009<br>Resumo: O objetivo desse trabalho é estudar as equações de Hamilton no contexto estocástico. Sendo necessário para tal um pouco de conhecimento a cerca dos seguintes assuntos: cálculo estocástico, geometria de segunda ordem, est
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5

Van, De Ven Christiaan Jozef Farielda. "Quantum Systems and their Classical Limit A C*- Algebraic Approach." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/324358.

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In this thesis we develop a mathematically rigorous framework of the so-called ''classical limit'' of quantum systems and their semi-classical properties. Our methods are based on the theory of strict, also called C*- algebraic deformation quantization. Since this C*-algebraic approach encapsulates both quantum as classical theory in one single framework, it provides, in particular, an excellent setting for studying natural emergent phenomena like spontaneous symmetry breaking (SSB) and phase transitions typically showing up in the classical limit of quantum theories. To this end, several tech
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6

Martin, Shaun K. "Symplectic geometry and gauge theory." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389209.

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7

Smith, Ivan. "Symplectic geometry of Lefschetz fibrations." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299234.

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8

Boalch, Philip Paul. "Symplectic geometry and isomonodromic deformations." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301848.

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9

at, Andreas Cap@esi ac. "Equivariant Symplectic Geometry of Cotangent Bundles." Moscow Math. J. 1, No.2 (2001) 287-299, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi996.ps.

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10

Rødland, Lukas. "Symplectic geometry and Calogero-Moser systems." Thesis, Uppsala universitet, Teoretisk fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-256742.

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We introduce some basic concepts from symplectic geometry, classical mechanics and integrable systems. We use this theory to show that the rational and the trigonometric Calogero-Moser systems, that is the Hamiltonian systems with Hamiltonian <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H=%5Csum_%7Bi=1%7D%5En%20p_i%5E2-%5Csum_%7Bj%5Cneq%20i%7D%20%5Cfrac%7B1%7D%7B(x_i-x_j)%5E2%7D%20" /> and <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H=%5Csum_i%20p_%7Bi%7D+%5Csum_%7Bi%5Cneq%20j%7D%20%5Cfrac%7B1%7D%7B4%20%5Csin%20%5E2((x_%7Bi%7D-x_%7Bj%7D)/2)%7D" /> respectively are inte
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11

Karlsson, Jesper. "Symplectic Automorphisms of C2n." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-144390.

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This essay is a detailed survey of an article from 1996 published by Franc Forstneric, where he studies symplectic automorphisms of C2n. The vision is to introduce the density property for holomorphic symplectic manifolds. Our idea is that of Dror Varolin when he in 2001 introduced the concept of density property for Stein manifolds. The main result here is the introduction of symplectic shears on C2n equipped with a holomorphic symplectic form and to show that the group generated by finite compositions of symplectic shears is dense in the group of symplectic automorphisms of C2n in the compac
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12

Ishikawa, Suguru. "Construction of general symplectic field theory." Kyoto University, 2019. http://hdl.handle.net/2433/242575.

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13

Balleier, Carsten. "Geometry and quantization of Howe pairs of symplectic actions." Thesis, Metz, 2009. http://www.theses.fr/2009METZ016S/document.

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Motivé par la dualité de Howe dans la théorie des représentations de groupes de Lie, on cherche une construction analogue en géométrie symplectique, c'est-à-dire on souhaite que sa quantification géométrique décomposé de manière Howe-duale. On trouve que dans le contexte symplectique, le cadre correct est donné par deux groupes de Lie agissant sur la même variété symplectique si ces actions commutent et satisfont la condition de Howe symplectique, i. e., ces actions sont hamiltoniennes et leurs fonctions collectives sont leurs centralisateurs mutuelles dans l'algèbre de Poisson des fonctions l
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14

Distexhe, Julie. "Triangulating symplectic manifolds." Doctoral thesis, Universite Libre de Bruxelles, 2019. https://dipot.ulb.ac.be/dspace/bitstream/2013/287522/3/toc.pdf.

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Le but de cette thèse est d'étudier les structures symplectiques dans la catégorie des variétés linéaires par morceaux (PL). La question centrale est de déterminer si toute variété symplectique lisse $(M,omega)$ peut être triangulée de manière symplectique, au sens où il existe une variété linéaire par morceaux $K$ et une triangulation $h :K -> M$ telle que $h^*omega$ est une forme symplectique constante par morceaux. Nous étudions d'abord un problème plus simple, qui consiste à trianguler les formes volumes lisses. Étant donnée une variété lisse $M$ munie d'une forme volume $Omega$, nous mont
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15

CATTANEO, ALBERTO. "NON-SYMPLECTIC AUTOMORPHISMS OF IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/606455.

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La tesi si concentra sullo studio degli automorfismi di varietà olomorfe simplettiche irriducibili di tipo K3^[n], ovvero varietà equivalenti per deformazione allo schema di Hilbert di n punti su una superficie K3, per n > 1. Negli ultimi anni, molti teoremi classici riguardanti la classificazione degli automorfismi non-simplettici di superfici K3 sono stati estesi alle varietà di tipo K3^[2]. Siamo quindi interessati a comprendere se tali risultati possono essere ulteriormente generalizzati anche al caso di varietà di tipo K3^[n], per n > 2. Nella prima parte della tesi descriviamo il grup
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16

Bussi, Vittoria. "Derived symplectic structures in generalized Donaldson-Thomas theory and categorification." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:54896cc4-b3fa-4d93-9fa9-2a842ad5e4df.

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This thesis presents a series of results obtained in [13, 18, 19, 23{25, 87]. In [19], we prove a Darboux theorem for derived schemes with symplectic forms of degree k < 0, in the sense of [142]. We use this to show that the classical scheme X = t<sub>0</sub>(X) has the structure of an algebraic d-critical locus, in the sense of Joyce [87]. Then, if (X, s) is an oriented d-critical locus, we prove in [18] that there is a natural perverse sheaf P·<sub>X,s</sub> on X, and in [25], we construct a natural motive MF<sub>X,s</sub>, in a certain quotient ring M<sup>μ</sup><sub>X</sub> of the μ-equiva
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17

Lozano, Guadalupe I. "Poisson geometry of the Ablowitz-Ladik equations." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/290120.

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This research seeks to understand the Poisson Geometry of the Ablowitz-Ladik equations (AL), an integrable discretization of the Non-linear Schrodinger equation (NLS) first proposed by Ablowitz and Ladik in the 70's. More specifically, to argue that the AL hierarchy (an integrable hierarchy of equations which comprises AL) can be explicitly viewed as a hierarchy of commuting flows which: (1) are Hamiltonian with respect to both a (known) Poisson operator J, and a (new) non-local, skew, almost Poisson operator K, on the appropriate space; (2) can be recursively generated from an operator R = KJ
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18

Kourliouros, Konstantinos. "Boundary singularities of functions in symplectic and volume-preserving geometry." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/32268.

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In this thesis we study the classi cation problem of boundary singularities of functions in symplectic and volume-preserving geometry. In particular we generalise several well known theorems concerning the classi cation of isolated singularities of functions and volume forms in the presence of a \boundary", i.e. a germ of a xed smooth hypersurface. The results depend in turn on a generalisation of the relative de Rham cohomology and the corresponding Gauss-Manin theory to the case of isolated boundary singularities and in particular, on a relative version of the so called Brieskorn-Deligne-Seb
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19

de, Gosson de Varennes Serge. "Multi-oriented Symplectic Geometry and the Extension of Path Intersection Indices." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-400.

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Symplectic geometry can be traced back to Lagrange and his work on celestial mechanics and has since then been a very active field in mathematics, partly because of the applications it offers but also because of the beauty of the objects it deals with. I this thesis we begin by the simplest fact of symplectic geometry. We give the definition of a symplectic space and of the symplectic group, Sp(n). A symplectic space is the data of an even-dimensional space and of a form which satisfies a number of properties. Having done this we give a definition of the Lagrangian Grassmannian Lag(n) which co
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20

Melani, Valerio. "Poisson and coisotropic structures in derived algebraic geometry." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC299/document.

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Dans cette thèse, on définit et on étudie les notions de structure de Poisson et coïsotrope sur un champ dérivé, dans le contexte de la géométrie algébrique dérivée. On considère deux présentations différentes de structure de Poisson : la première est purement algébrique, alors que la deuxième est plus géométrique. On montre que les deux approches sont en fait équivalentes. On introduit aussi la notion de structure coïsotrope sur un morphisme de champs dérivés, encore une fois en présentant deux définitions équivalentes : la première est basée sur une généralisation appropriée de l'opérade Swi
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21

Richard, Nicolas. "Extrinsic symmetric symplectic spaces." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210064.

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Résumé de la thèse :ce travail porte sur la notion d'espace symétrique symplectique extrinsèque. Ces espaces sont des espaces symétriques symplectiques dont la structure est induite par le plongement dans variété symplectique ambiante munie d'une connexion.<p><p>Par analogie à la théorie standard des espaces symétriques, nous démontrons un théorème d'équivalence entre les espaces symétriques symplectiques extrinsèques d'une variété qui est elle-même un espace symétrique symplectique.<p><p>La définition d'un espace symétrique symplectique extrinsèque fait intervenir l'existence d'affinités glob
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22

Cattaneo, Alberto. "Non-symplectic automorphisms of irreducible holomorphic symplectic manifolds." Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2322/document.

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Nous allons étudier les automorphismes des variétés symplectiques holomorphes irréductibles de type K3^[n], c'est-à-dire des variétés équivalentes par déformation au schéma de Hilbert de n points sur une surface K3, pour n &gt; 1.Dans la première partie de la thèse, nous classifions les automorphismes du schéma de Hilbert de n points sur une surface K3 projective générique, dont le réseau de Picard est engendré par un fibré ample. Nous montrons que le groupe des automorphismes est soit trivial soit engendré par une involution non-symplectique et nous déterminons des conditions numériques et gé
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23

Gosson, Maurice A. de. "Symplectic geometry, Wigner-Weyl-Moyal calculus, and quantum mechanics in phase space." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3021/.

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Contents: Part I: Symplectic Geometry Chapter 1: Symplectic Spaces and Lagrangian Planes Chapter 2: The Symplectic Group Chapter 3: Multi-Oriented Symplectic Geometry Chapter 4: Intersection Indices in Lag(n) and Sp(n) Part II: Heisenberg Group, Weyl Calculus, and Metaplectic Representation Chapter 5: Lagrangian Manifolds and Quantization Chapter 6: Heisenberg Group and Weyl Operators Chapter 7: The Metaplectic Group Part III: Quantum Mechanics in Phase Space Chapter 8: The Uncertainty Principle Chapter 9: The Density Operator Chapter 10: A Phase Space Weyl Calculus
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24

Russell, Neil Eric. "Aspects of the symplectic and metric geometry of classical and quantum physics." Thesis, Rhodes University, 1993. http://hdl.handle.net/10962/d1005237.

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I investigate some algebras and calculi naturally associated with the symplectic and metric Clifford algebras. In particular, I reformulate the well known Lepage decomposition for the symplectic exterior algebra in geometrical form and present some new results relating to the simple subspaces of the decomposition. I then present an analogous decomposition for the symmetric exterior algebra with a metric. Finally, I extend this symmetric exterior algebra into a new calculus for the symmetric differential forms on a pseudo-Riemannian manifold. The importance of this calculus lies in its potentia
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25

Narayanan, Vivek. "Some aspects of the geometry of Poisson dynamical systems." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3038192.

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26

Gardell, Fredrik. "Geometric Quantization." Thesis, Uppsala universitet, Teoretisk fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296618.

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In this project we introduce the general idea of geometric quantization and demonstratehow to apply the process on a few examples. We discuss how to construct a line bundleover the symplectic manifold with Dirac’s quantization conditions and how to determine if we are able to quantize a system with the help of Weil’s integrability condition. To reducethe prequantum line bundle we employ real polarization such that the system does notbreak Heisenberg’s uncertainty principle anymore. From the prequantum bundle and thepolarization we construct the sought after Hilbert space.
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27

Prüfer, Sven [Verfasser], and Kai [Akademischer Betreuer] Cieliebak. "Symplectic Geometry of Moduli Spaces of Hurwitz Covers / Sven Prüfer ; Betreuer: Kai Cieliebak." Augsburg : Universität Augsburg, 2017. http://d-nb.info/114485797X/34.

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28

Zinger, Aleksey 1975. "Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/8402.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.<br>Includes bibliographical references (p. 239-240).<br>Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in symplectic topology and its influence on enumerative geometry. The most straightforward applications of the methods developed are to enumeration of rational curves with a cusp of specified nature in projective spaces. A general approach for
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29

Caine, John Arlo. "Poisson Structures on U/K and Applications." Diss., The University of Arizona, 2007. http://hdl.handle.net/10150/195363.

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Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let g denote the complexification of the Lie algebra of U, g=u^C. Each u-compatible triangular decomposition g= n_- + h + n_+ determines a Poisson Lie group structure pi_U on U. The Evens-Lu construction produces a (U, pi_U)-homogeneous Poisson structure on X. By choosing the basepoint in X appropriately, X is presented as U/K where K is the fixed point set of an involution which stabilizes the triangular decomposition of g. With this
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30

FOSSATI, Edoardo. "Symplectic fillings of virtually overtwisted contact structures on lens spaces." Doctoral thesis, Scuola Normale Superiore, 2020. http://hdl.handle.net/11384/90719.

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Symplectic fillings of standard tight contact structures on lens spaces are understood and classified. The situation is different if one considers non-standard tight structures (i.e. those that are virtually overtwisted), for which a classification scheme is still missing. In this work we use different approaches and employ various techniques to improve our knowledge of symplectic fillings of virtually overtwisted contact structures. We study curves configurations on surfaces to solve the problem in the case of a specific family of lens spaces. Then we give general constraints on the top
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31

Bott, Christopher James. "Mirror Symmetry for K3 Surfaces with Non-symplectic Automorphism." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7456.

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Mirror symmetry is the phenomenon, originally discovered by physicists, that Calabi-Yau manifolds come in dual pairs, with each member of the pair producing the same physics. Mathematicians studying enumerative geometry became interested in mirror symmetry around 1990, and since then, mirror symmetry has become a major research topic in pure mathematics. One important problem in mirror symmetry is that there may be several ways to construct a mirror dual for a Calabi-Yau manifold. Hence it is a natural question to ask: when two different mirror symmetry constructions apply, do they agree?We sp
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32

Bäck, Viktor. "Localization of Multiscale Screened Poisson Equation." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-180928.

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33

NOVARIO, SIMONE. "LINEAR SYSTEMS ON IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/886303.

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In questa tesi studiamo alcuni sistemi lineari completi associati a divisori di schemi di Hilbert di 2 punti su una superficie K3 proiettiva complessa con gruppo di Picard di rango 1, e le mappe razionali indotte. Queste varietà sono chiamate quadrati di Hilbert su superfici K3 generiche, e sono esempi di varietà irriducibili olomorfe simplettiche (varietà IHS). Nella prima parte della tesi, usando la teoria dei reticoli, gli operatori di Nakajima e il modello di Lehn–Sorger, diamo una base per il sottospazio vettoriale dell’anello di coomologia singolare a coefficienti razionali generato dal
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34

Saha, Chiranjib. "Advances in Stochastic Geometry for Cellular Networks." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99835.

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The mathematical modeling and performance analysis of cellular networks have seen a major paradigm shift with the application of stochastic geometry. The main purpose of stochastic geometry is to endow probability distributions on the locations of the base stations (BSs) and users in a network, which, in turn, provides an analytical handle on the performance evaluation of cellular networks. To preserve the tractability of analysis, the common practice is to assume complete spatial randomness} of the network topology. In other words, the locations of users and BSs are modeled as independent hom
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35

Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.

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This thesis primarily discusses the results of two papers, [Hu] and [HaHu]. The first is an overview of algebraic-geometric techniques for integrable systems in which the AKS theorem is proven. Under certain conditions, this theorem asserts the commutatvity and (potential) non-triviality of the Hamiltonian flow of Ad*-invariant functions once they're restricted to subalgebras. This theorem is applied to the case of coadjoint orbits on loop algebras, identifying the flow with a spectral curve and a line bundle via the Lax equation. These results play an important role in the discussion of [HaHu
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36

Aravanis, Alexios. "Closed form analysis of Poisson cellular networks: a stochastic geometry approach." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/667470.

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Ultra dense networks (UDNs) allow for efficient spatial reuse of the spectrum, giving rise to substantial capacity and power gains. In order to exploit those gains, tractable mathematical models need to be derived, allowing for the analysis and optimization of the network operation. In this course, stochastic geometry has emerged as a powerful tool for large-scale analysis and modeling of wireless cellular networks. In particular, the employment of stochastic geometry has been proven instrumental for the characterization of the network performance and for providing significant insights into ne
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37

Sugimoto, Yoshihiro. "Spectral spread and non-autonomous Hamiltonian diffeomorphisms." Kyoto University, 2019. http://hdl.handle.net/2433/242579.

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38

Lamb, McKenzie Russell. "Ginzburg-Weinstein Isomorphisms for Pseudo-Unitary Groups." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/193755.

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Ginzburg and Weinstein proved in [GW92] that for a compact, semisimple Lie group K endowed with the Lu-Weinstein Poisson structure, there exists a Poisson diffeomorphism from the dual Poisson Lie group K* to the dual k* of the Lie algebra of K endowed with the Lie-Poisson structure. We investigate the possibility of extending this result to the pseudo-unitary groups SU (p, q ), which are semisimple but not compact. The main results presented here are the following. (1) The Ginzburg-Weinstein proof hinges on the existence of a certain vector field X on k*. We prove that for any p, q, the analo
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Chetlur, Ravi Vishnu Vardhan. "Stochastic Geometry for Vehicular Networks." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99954.

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Vehicular communication networks are essential to the development of intelligent navigation systems and improvement of road safety. Unlike most terrestrial networks of today, vehicular networks are characterized by stringent reliability and latency requirements. In order to design efficient networks to meet these requirements, it is important to understand the system-level performance of vehicular networks. Stochastic geometry has recently emerged as a powerful tool for the modeling and analysis of wireless communication networks. However, the canonical spatial models such as the 2D Poisson po
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40

Benedetti, Gabriele. "The contact property for magnetic flows on surfaces." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247157.

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This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is the surface, g is the metric and σ is a 2-form on M . Such dynamical systems are described by the Hamiltonian equations of a function E on the tangent bundle TM endowed with a symplectic form ω_σ, where E is the kinetic energy. Our main goal is to prove existence results for a) periodic orbits, and b) Poincare sections for motions on a fixed energy level Σ_m := {E = m^2/2} ⊂ T M . We tackle this problem by studying the contact geometry of t
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41

Lemes, Ricardo Chicalé [UNESP]. "Propriedades genéricas de sistemas hamiltonianos." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/111007.

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Made available in DSpace on 2014-12-02T11:16:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-12-05Bitstream added on 2014-12-02T11:21:26Z : No. of bitstreams: 1 000793711.pdf: 1081771 bytes, checksum: 9ad4a08d3ec9d6accf66ef005a138f0a (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Nosso objetivo neste trabalho é demonstrar o Teorema da Densidade Geral que é um resultado análogo ao Teorema de Kupka-Smale para campos de vetores hamiltonianos. O Teorema da Densidade Geral afirma que o conjuntos dos campos hamiltonianos em uma variedade simplética M que
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Lemes, Ricardo Chicalé. "Propriedades genéricas de sistemas hamiltonianos /." São José do Rio Preto, 2013. http://hdl.handle.net/11449/111007.

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Orientador: Vanderlei Minori Horita<br>Banca: Thiago Aparecido Catalan<br>Banca: Claudio Aguinaldo Buzzi<br>Resumo: Nosso objetivo neste trabalho é demonstrar o Teorema da Densidade Geral que é um resultado análogo ao Teorema de Kupka-Smale para campos de vetores hamiltonianos. O Teorema da Densidade Geral afirma que o conjuntos dos campos hamiltonianos em uma variedade simplética M que possuem a propriedade H2-N é residual em Xk H(M). Começamos estabelecendo as teorias simpléticas linear e não-linear básicas e depois estudamos suas conexões com os sistemas hamiltonianos, provando os principai
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43

Guan, Peng. "Stochastic Geometry Analysis of LTE-A Cellular Networks." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS252/document.

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L’objectif principal de cette thèse est l’analyse des performances des réseaux LTE-A (Long Term Evolution- Advanced) au travers de la géométrie stochastique. L’analyse mathématique des réseaux cellulaires est un problème difficile, pour lesquels ils existent déjà un certain nombre de résultats mais qui demande encore des efforts et des contributions sur le long terme. L’utilisation de la géométrie aléatoire et des processus ponctuels de Poisson (PPP) s’est avérée être une approche permettant une modélisation pertinente des réseaux cellulaires et d’une complexité faible (tractable). Dans cette
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44

Spiegler, Adam. "Stability of Generic Equilibria of the 2n Dimensional Free Rigid Body Using the Energy-Casimir Method." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/194821.

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The rigid body has been one of the most noteworthy applications of Newtonian mechanics. Applying the principles of classical mechanics to the rigid body is by no means routine. The equations of motion, though discovered two hundred and fifty years ago by Euler, have remained quite elusive since their introduction. Understanding the rigid body has required the applications of concepts from integrable systems, algebraic geometry, Lie groups, representation theory, and symplectic geometry to name a few. Moreover, several important developments in these fields have in fact originated with the stu
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45

Sáez, Calvo Carles. "Finite groups acting on smooth and symplectic 4-manifolds." Doctoral thesis, Universitat de Barcelona, 2019. http://hdl.handle.net/10803/667781.

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En esta tesis se estudian problemas relacionados con acciones de grupos finitos en 4-variedades diferenciables y simplécticas. Se prueba que toda 4-variedad diferenciable cerrada X admite una constante C>0 tal que cualquier grupo finito G que actúa en X de manera efectiva y diferenciable tiene un subgrupo H abeliano o nilpotente de clase 2 que satisface [G:H]<C. Se da una caracterización parcial de las 4-variedades cerradas con grupo de difeomorfismos Jordan. Se prueba también que toda 4-variedad cuasi compleja cerrada tiene grupo de automorfismos Jordan y que toda 4-variedad simpléctica cerra
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Roeser, Markus Karl. "The ASD equations in split signature and hypersymplectic geometry." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:7d46ffc8-6d12-4fec-9450-13d2c726885c.

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This thesis is mainly concerned with the study of hypersymplectic structures in gauge theory. These structures arise via applications of the hypersymplectic quotient construction to the action of the gauge group on certain spaces of connections and Higgs fields. Motivated by Kobayashi-Hitchin correspondences in the case of hyperkähler moduli spaces, we first study the relationship between hypersymplectic, complex and paracomplex quotients in the spirit of Kirwan's work relating Kähler quotients to GIT quotients. We then study dimensional reductions of the ASD equations on $mathbb R^{2,2}$. We
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Chapron, Aurélie. "Mosaïques de Poisson-Voronoï sur une variété riemannienne." Thesis, Paris 10, 2018. http://www.theses.fr/2018PA100098/document.

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Une mosaïque de Poisson-Voronoï est une partition aléatoire de l'espace euclidien en polyèdres, appelés cellules, obtenue à partir d'un ensemble aléatoire discret de points appelés germes. A chaque germe correspond une cellule, qui est l'ensemble des points de l'espace qui sont plus proches de ce germes que des autres germes. Ces modèles sont souvent utilisées dans divers domaines tels que la biologie, les télécommunications, l'astronomie, etc. Les caractéristiques de ces mosaïques et des cellules associées ont été largement étudiées dans l'espace euclidien mais les travaux sur les mosaïques d
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Singh, Javed Kiran. "Topics in the geometry and physics of Galilei invariant quantum and classical dynamics." Thesis, University of Hull, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342978.

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49

Bergvall, Olof. "Cohomology of the moduli space of curves of genus three with level two structure." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-103062.

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In this thesis we investigate the moduli space M3[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M3[2] into a disjoint union of two natural subspaces, Q[2] and H3[2], and then making S7- resp. S8-equivariantpoint counts of each of these spaces separately.<br>Målet med denna uppsats är att undersöka modulirummet M3[2] av kurvor av genus 3 med symplektisk nivå 2 struktur. Mer specifikt vill vi hitta informationom kohomologin av detta rum. För att uppnå detta
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Song, Jian. "A Stochastic Geometry Approach to the Analysis and Optimization of Cellular Networks." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS545.

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Cette thèse porte principalement sur la modélisation, l'évaluation des performances et l'optimisation au niveau système des réseaux cellulaires de nouvelle génération à l'aide de la géométrie stochastique. En plus, la technologie émergente des surfaces intelligentes reconfigurables (RISs) est étudiée pour l'application aux futurs réseaux sans fil. En particulier, reposant sur un modèle d’abstraction basé sur la loi de Poisson pour la distribution spatiale des nœuds et des points d’accès, cette thèse développe un ensemble de nouveaux cadres analytiques pour le calcul d’importantes métriques de
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